Abstract
In this paper, we investigate special Smarandache curves with regard to Sabban frame for Bertrand partner curve spherical indicatrix. Some results have been obtained. These results were expressed depending on the Bertrand curve. Besides, we are given examples of our results.
Highlights
We have an orthonormal frame {T, N, B} along α
We have the following spherical Frenet formulae of γ γ′(s) = t(s), t′(s) = −γ(s) + κg (s)d(s), d′(s) = −κg (s)t(s) where κg is called the geodesic curvature of the curve γ on S2 which is κg(s) = t′(s), d(s), [11]
We investigate special Smarandache curves created by Sabban frame, {T ∗, TT ∗, T ∗ belongs to spherical
Summary
We have an orthonormal frame {T, N, B} along α. We have the following spherical Frenet formulae of γ γ′(s) = t(s), t′(s) = −γ(s) + κg (s)d(s), d′(s) = −κg (s)t(s) where κg is called the geodesic curvature of the curve γ on S2 which is κg(s) = t′(s), d(s), [11]. Differentiating (2.16), we can write tan(φ − θ) sin θ − cos θ tan(φ − θ) tan(φ − θ) cos θ − sin θ
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